Question
Wed July 11, 2012 By:

Gravity at the centre of the earth for an object of mass m, GMm/R^2=GMm/0^2=undefined. How can it be 0?

Expert Reply
Thu July 12, 2012
gravyty at the centre of the earth should not be found by this formula as u have done:GMm/R^2=GMm/0^2=undefined.
As we go deep into the earth's surface, suppose at depth  d from the earth's surface, there the force will be applied by the portion of of radius (R-d) of earth . Not the whole earth.The outer shell will not apply any force on the object. so the gravity will decrease at a different rate as we go deep into the earth's surface.
There the calculatiopn will be according to:

Variation of 'g' with depth

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Variation of 'g' with depth

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Consider a body of mass m, lying on the surface of the Earth of radius R and mass M. Let g be the acceleration due to gravity at that place.

Let the body be taken to a depth d from the surface of the Earth. Then, the force due to gravity acting on this body is only due to the sphere of radius R.

(R - d). If g| is the acceleration due to gravity at depth 'd'

Let the Earth be of uniform density r and its shape be a perfect sphere.

(Where r is the density of the Earth)

Comparing g| and g

The acceleration due to gravity decreases with increase in depth.

If d = R, then g| = 0.

Weight of a body at the centre of the Earth is zero.

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